LMFDB - Embedded newform 85.2.e.a.21.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(21,85)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("85.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.6
Root			$0.254679i$ of defining polynomial
Character	$\chi$	$=$	85.21
Dual form			85.2.e.a.81.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.51230i q^{2} +(-0.887192 + 0.887192i) q^{3} -4.31167 q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.22889 - 2.22889i) q^{6} +(1.14187 + 1.14187i) q^{7} -5.80761i q^{8} +1.42578i q^{9} +(1.77647 + 1.77647i) q^{10} +(-2.32404 - 2.32404i) q^{11} +(3.82528 - 3.82528i) q^{12} +6.35524 q^{13} +(-2.86872 + 2.86872i) q^{14} +1.25468i q^{15} +5.96715 q^{16} +(-0.768287 + 4.05089i) q^{17} -3.58200 q^{18} -0.747167i q^{19} +(-3.04881 + 3.04881i) q^{20} -2.02612 q^{21} +(5.83869 - 5.83869i) q^{22} +(0.101240 + 0.101240i) q^{23} +(5.15247 + 5.15247i) q^{24} -1.00000i q^{25} +15.9663i q^{26} +(-3.92652 - 3.92652i) q^{27} +(-4.92337 - 4.92337i) q^{28} +(6.22477 - 6.22477i) q^{29} -3.15213 q^{30} +(5.10259 - 5.10259i) q^{31} +3.37606i q^{32} +4.12374 q^{33} +(-10.1771 - 1.93017i) q^{34} +1.61485 q^{35} -6.14750i q^{36} +(-0.439195 + 0.439195i) q^{37} +1.87711 q^{38} +(-5.63832 + 5.63832i) q^{39} +(-4.10660 - 4.10660i) q^{40} +(-4.49889 - 4.49889i) q^{41} -5.09022i q^{42} +2.74801i q^{43} +(10.0205 + 10.0205i) q^{44} +(1.00818 + 1.00818i) q^{45} +(-0.254346 + 0.254346i) q^{46} -11.9308 q^{47} +(-5.29400 + 5.29400i) q^{48} -4.39226i q^{49} +2.51230 q^{50} +(-2.91230 - 4.27554i) q^{51} -27.4017 q^{52} +2.71404i q^{53} +(9.86460 - 9.86460i) q^{54} -3.28669 q^{55} +(6.63154 - 6.63154i) q^{56} +(0.662880 + 0.662880i) q^{57} +(15.6385 + 15.6385i) q^{58} +12.6815i q^{59} -5.40976i q^{60} +(0.328162 + 0.328162i) q^{61} +(12.8193 + 12.8193i) q^{62} +(-1.62806 + 1.62806i) q^{63} +3.45261 q^{64} +(4.49384 - 4.49384i) q^{65} +10.3601i q^{66} +1.81686 q^{67} +(3.31260 - 17.4661i) q^{68} -0.179639 q^{69} +4.05699i q^{70} +(-3.01043 + 3.01043i) q^{71} +8.28039 q^{72} +(-0.856488 + 0.856488i) q^{73} +(-1.10339 - 1.10339i) q^{74} +(0.887192 + 0.887192i) q^{75} +3.22154i q^{76} -5.30750i q^{77} +(-14.1652 - 14.1652i) q^{78} +(-3.57000 - 3.57000i) q^{79} +(4.21941 - 4.21941i) q^{80} +2.68980 q^{81} +(11.3026 - 11.3026i) q^{82} -3.58494i q^{83} +8.73594 q^{84} +(2.32115 + 3.40767i) q^{85} -6.90384 q^{86} +11.0451i q^{87} +(-13.4971 + 13.4971i) q^{88} -10.5906 q^{89} +(-2.53285 + 2.53285i) q^{90} +(7.25687 + 7.25687i) q^{91} +(-0.436515 - 0.436515i) q^{92} +9.05395i q^{93} -29.9739i q^{94} +(-0.528327 - 0.528327i) q^{95} +(-2.99521 - 2.99521i) q^{96} +(-4.92762 + 4.92762i) q^{97} +11.0347 q^{98} +(3.31357 - 3.31357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) $ 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.51230i			1.77647i	0.459392	+	0.888233i	$0.348067\pi$
$2$			2.51230i			1.77647i	−0.459392	+	0.888233i	$0.651933\pi$
$3$	−0.887192	+	0.887192i	−0.512220	+	0.512220i	−0.915206	−	0.402986i	$-0.867972\pi$
$3$	−0.887192	+	0.887192i	−0.512220	+	0.512220i	0.402986	+	0.915206i	$0.367972\pi$
$4$	−4.31167			−2.15583
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−2.22889	−	2.22889i	−0.909943	−	0.909943i
$7$	1.14187	+	1.14187i	0.431586	+	0.431586i	0.889168	−	0.457581i	$-0.151284\pi$
$7$	1.14187	+	1.14187i	0.431586	+	0.431586i	−0.457581	+	0.889168i	$0.651284\pi$
$8$		−	5.80761i		−	2.05330i
$9$			1.42578i			0.475261i
$10$	1.77647	+	1.77647i	0.561768	+	0.561768i
$11$	−2.32404	−	2.32404i	−0.700724	−	0.700724i	0.263842	−	0.964566i	$-0.415010\pi$
$11$	−2.32404	−	2.32404i	−0.700724	−	0.700724i	−0.964566	+	0.263842i	$0.915010\pi$
$12$	3.82528	−	3.82528i	1.10426	−	1.10426i
$13$	6.35524			1.76263			0.881314	−	0.472531i	$-0.156660\pi$
$13$	6.35524			1.76263			0.881314	+	0.472531i	$0.156660\pi$
$14$	−2.86872	+	2.86872i	−0.766699	+	0.766699i
$15$			1.25468i			0.323957i
$16$	5.96715			1.49179
$17$	−0.768287	+	4.05089i	−0.186337	+	0.982486i
$17$	−0.768287	+	4.05089i	−0.186337	+	0.982486i
$18$	−3.58200			−0.844284
$19$		−	0.747167i		−	0.171412i	−0.996320	−	0.0857059i	$-0.972685\pi$
$19$		−	0.747167i		−	0.171412i	0.996320	−	0.0857059i	$-0.0273145\pi$
$20$	−3.04881	+	3.04881i	−0.681735	+	0.681735i
$21$	−2.02612			−0.442135
$22$	5.83869	−	5.83869i	1.24481	−	1.24481i
$23$	0.101240	+	0.101240i	0.0211101	+	0.0211101i	0.717583	−	0.696473i	$-0.245248\pi$
$23$	0.101240	+	0.101240i	0.0211101	+	0.0211101i	−0.696473	+	0.717583i	$0.745248\pi$
$24$	5.15247	+	5.15247i	1.05174	+	1.05174i
$25$		−	1.00000i		−	0.200000i
$26$			15.9663i			3.13125i
$27$	−3.92652	−	3.92652i	−0.755659	−	0.755659i
$28$	−4.92337	−	4.92337i	−0.930429	−	0.930429i
$29$	6.22477	−	6.22477i	1.15591	−	1.15591i	0.170565	−	0.985346i	$-0.445441\pi$
$29$	6.22477	−	6.22477i	1.15591	−	1.15591i	0.985346	−	0.170565i	$-0.0545592\pi$
$30$	−3.15213			−0.575498
$31$	5.10259	−	5.10259i	0.916452	−	0.916452i	−0.0803174	−	0.996769i	$-0.525593\pi$
$31$	5.10259	−	5.10259i	0.916452	−	0.916452i	0.996769	+	0.0803174i	$0.0255934\pi$
$32$			3.37606i			0.596809i
$33$	4.12374			0.717850
$34$	−10.1771	−	1.93017i	−1.74535	−	0.331021i
$35$	1.61485			0.272959
$36$		−	6.14750i		−	1.02458i
$37$	−0.439195	+	0.439195i	−0.0722032	+	0.0722032i	−0.742286	−	0.670083i	$-0.766258\pi$
$37$	−0.439195	+	0.439195i	−0.0722032	+	0.0722032i	0.670083	+	0.742286i	$0.266258\pi$
$38$	1.87711			0.304507
$39$	−5.63832	+	5.63832i	−0.902854	+	0.902854i
$40$	−4.10660	−	4.10660i	−0.649311	−	0.649311i
$41$	−4.49889	−	4.49889i	−0.702609	−	0.702609i	0.262361	−	0.964970i	$-0.415499\pi$
$41$	−4.49889	−	4.49889i	−0.702609	−	0.702609i	−0.964970	+	0.262361i	$0.915499\pi$
$42$		−	5.09022i		−	0.785438i
$43$			2.74801i			0.419068i	0.977801	+	0.209534i	$0.0671947\pi$
$43$			2.74801i			0.419068i	−0.977801	+	0.209534i	$0.932805\pi$
$44$	10.0205	+	10.0205i	1.51064	+	1.51064i
$45$	1.00818	+	1.00818i	0.150291	+	0.150291i
$46$	−0.254346	+	0.254346i	−0.0375013	+	0.0375013i
$47$	−11.9308			−1.74029			−0.870146	−	0.492794i	$-0.835976\pi$
$47$	−11.9308			−1.74029			−0.870146	+	0.492794i	$0.835976\pi$
$48$	−5.29400	+	5.29400i	−0.764124	+	0.764124i
$49$		−	4.39226i		−	0.627466i
$50$	2.51230			0.355293
$51$	−2.91230	−	4.27554i	−0.407804	−	0.598695i
$52$	−27.4017			−3.79993
$53$			2.71404i			0.372802i	0.982474	+	0.186401i	$0.0596823\pi$
$53$			2.71404i			0.372802i	−0.982474	+	0.186401i	$0.940318\pi$
$54$	9.86460	−	9.86460i	1.34240	−	1.34240i
$55$	−3.28669			−0.443177
$56$	6.63154	−	6.63154i	0.886177	−	0.886177i
$57$	0.662880	+	0.662880i	0.0878006	+	0.0878006i
$58$	15.6385	+	15.6385i	2.05344	+	2.05344i
$59$			12.6815i			1.65099i	0.564413	+	0.825493i	$0.309103\pi$
$59$			12.6815i			1.65099i	−0.564413	+	0.825493i	$0.690897\pi$
$60$		−	5.40976i		−	0.698397i
$61$	0.328162	+	0.328162i	0.0420168	+	0.0420168i	0.727803	−	0.685786i	$-0.240542\pi$
$61$	0.328162	+	0.328162i	0.0420168	+	0.0420168i	−0.685786	+	0.727803i	$0.740542\pi$
$62$	12.8193	+	12.8193i	1.62805	+	1.62805i
$63$	−1.62806	+	1.62806i	−0.205116	+	0.205116i
$64$	3.45261			0.431576
$65$	4.49384	−	4.49384i	0.557392	−	0.557392i
$66$			10.3601i			1.27524i
$67$	1.81686			0.221965			0.110982	−	0.993822i	$-0.464600\pi$
$67$	1.81686			0.221965			0.110982	+	0.993822i	$0.464600\pi$
$68$	3.31260	−	17.4661i	0.401712	−	2.11808i
$69$	−0.179639			−0.0216260
$70$			4.05699i			0.484903i
$71$	−3.01043	+	3.01043i	−0.357272	+	0.357272i	−0.862806	−	0.505535i	$-0.831295\pi$
$71$	−3.01043	+	3.01043i	−0.357272	+	0.357272i	0.505535	+	0.862806i	$0.331295\pi$
$72$	8.28039			0.975853
$73$	−0.856488	+	0.856488i	−0.100244	+	0.100244i	−0.755450	−	0.655206i	$-0.772582\pi$
$73$	−0.856488	+	0.856488i	−0.100244	+	0.100244i	0.655206	+	0.755450i	$0.272582\pi$
$74$	−1.10339	−	1.10339i	−0.128267	−	0.128267i
$75$	0.887192	+	0.887192i	0.102444	+	0.102444i
$76$			3.22154i			0.369535i
$77$		−	5.30750i		−	0.604846i
$78$	−14.1652	−	14.1652i	−1.60389	−	1.60389i
$79$	−3.57000	−	3.57000i	−0.401656	−	0.401656i	0.477160	−	0.878816i	$-0.341666\pi$
$79$	−3.57000	−	3.57000i	−0.401656	−	0.401656i	−0.878816	+	0.477160i	$0.841666\pi$
$80$	4.21941	−	4.21941i	0.471744	−	0.471744i
$81$	2.68980			0.298867
$82$	11.3026	−	11.3026i	1.24816	−	1.24816i
$83$		−	3.58494i		−	0.393498i	−0.980454	−	0.196749i	$-0.936962\pi$
$83$		−	3.58494i		−	0.393498i	0.980454	−	0.196749i	$-0.0630385\pi$
$84$	8.73594			0.953169
$85$	2.32115	+	3.40767i	0.251764	+	0.369614i
$86$	−6.90384			−0.744460
$87$			11.0451i			1.18416i
$88$	−13.4971	+	13.4971i	−1.43880	+	1.43880i
$89$	−10.5906			−1.12260			−0.561300	−	0.827613i	$-0.689698\pi$
$89$	−10.5906			−1.12260			−0.561300	+	0.827613i	$0.689698\pi$
$90$	−2.53285	+	2.53285i	−0.266986	+	0.266986i
$91$	7.25687	+	7.25687i	0.760726	+	0.760726i
$92$	−0.436515	−	0.436515i	−0.0455098	−	0.0455098i
$93$			9.05395i			0.938851i
$94$		−	29.9739i		−	3.09157i
$95$	−0.528327	−	0.528327i	−0.0542052	−	0.0542052i
$96$	−2.99521	−	2.99521i	−0.305698	−	0.305698i
$97$	−4.92762	+	4.92762i	−0.500324	+	0.500324i	−0.911539	−	0.411215i	$-0.865105\pi$
$97$	−4.92762	+	4.92762i	−0.500324	+	0.500324i	0.411215	+	0.911539i	$0.365105\pi$
$98$	11.0347			1.11467
$99$	3.31357	−	3.31357i	0.333026	−	0.333026i
$100$			4.31167i			0.431167i
$101$	−0.679421			−0.0676049			−0.0338025	−	0.999429i	$-0.510762\pi$
$101$	−0.679421			−0.0676049			−0.0338025	+	0.999429i	$0.510762\pi$
$102$	10.7414	−	7.31658i	1.06356	−	0.724450i
$103$	−0.156455			−0.0154160			−0.00770798	−	0.999970i	$-0.502454\pi$
$103$	−0.156455			−0.0154160			−0.00770798	+	0.999970i	$0.502454\pi$
$104$		−	36.9088i		−	3.61921i
$105$	−1.43268	+	1.43268i	−0.139815	+	0.139815i
$106$	−6.81849			−0.662270
$107$	12.7033	−	12.7033i	1.22807	−	1.22807i	0.263382	−	0.964692i	$-0.415162\pi$
$107$	12.7033	−	12.7033i	1.22807	−	1.22807i	0.964692	−	0.263382i	$-0.0848379\pi$
$108$	16.9298	+	16.9298i	1.62907	+	1.62907i
$109$	4.10981	+	4.10981i	0.393649	+	0.393649i	0.875986	−	0.482337i	$-0.160212\pi$
$109$	4.10981	+	4.10981i	0.393649	+	0.393649i	−0.482337	+	0.875986i	$0.660212\pi$
$110$		−	8.25715i		−	0.787289i
$111$		−	0.779300i		−	0.0739679i
$112$	6.81371	+	6.81371i	0.643835	+	0.643835i
$113$	−6.57408	−	6.57408i	−0.618438	−	0.618438i	0.326693	−	0.945131i	$-0.394066\pi$
$113$	−6.57408	−	6.57408i	−0.618438	−	0.618438i	−0.945131	+	0.326693i	$0.894066\pi$
$114$	−1.66536	+	1.66536i	−0.155975	+	0.155975i
$115$	0.143175			0.0133512
$116$	−26.8392	+	26.8392i	−2.49195	+	2.49195i
$117$			9.06119i			0.837707i
$118$	−31.8597			−2.93292
$119$	−5.50288	+	3.74831i	−0.504448	+	0.343607i
$120$	7.28669			0.665180
$121$		−	0.197689i		−	0.0179717i
$122$	−0.824442	+	0.824442i	−0.0746414	+	0.0746414i
$123$	7.98276			0.719781
$124$	−22.0007	+	22.0007i	−1.97572	+	1.97572i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−4.09017	−	4.09017i	−0.364382	−	0.364382i
$127$			15.1796i			1.34698i	0.739198	+	0.673488i	$0.235205\pi$
$127$			15.1796i			1.34698i	−0.739198	+	0.673488i	$0.764795\pi$
$128$			15.4261i			1.36349i
$129$	−2.43801	−	2.43801i	−0.214655	−	0.214655i
$130$	11.2899	+	11.2899i	0.990188	+	0.990188i
$131$	1.40184	−	1.40184i	0.122480	−	0.122480i	−0.643210	−	0.765690i	$-0.722398\pi$
$131$	1.40184	−	1.40184i	0.122480	−	0.122480i	0.765690	+	0.643210i	$0.222398\pi$
$132$	−17.7802			−1.54757
$133$	0.853168	−	0.853168i	0.0739790	−	0.0739790i
$134$			4.56450i			0.394313i
$135$	−5.55293			−0.477920
$136$	23.5260	+	4.46191i	2.01734	+	0.382606i
$137$	19.6088			1.67530			0.837648	−	0.546211i	$-0.183930\pi$
$137$	19.6088			1.67530			0.837648	+	0.546211i	$0.183930\pi$
$138$		−	0.451308i		−	0.0384179i
$139$	−2.55364	+	2.55364i	−0.216597	+	0.216597i	−0.807063	−	0.590466i	$-0.798944\pi$
$139$	−2.55364	+	2.55364i	−0.216597	+	0.216597i	0.590466	+	0.807063i	$0.298944\pi$
$140$	−6.96269			−0.588455
$141$	10.5849	−	10.5849i	0.891413	−	0.891413i
$142$	−7.56310	−	7.56310i	−0.634681	−	0.634681i
$143$	−14.7698	−	14.7698i	−1.23512	−	1.23512i
$144$			8.50785i			0.708987i
$145$		−	8.80316i		−	0.731062i
$146$	−2.15176	−	2.15176i	−0.178081	−	0.178081i
$147$	3.89678	+	3.89678i	0.321401	+	0.321401i
$148$	1.89366	−	1.89366i	0.155658	−	0.155658i
$149$	−1.26402			−0.103553			−0.0517763	−	0.998659i	$-0.516488\pi$
$149$	−1.26402			−0.103553			−0.0517763	+	0.998659i	$0.516488\pi$
$150$	−2.22889	+	2.22889i	−0.181989	+	0.181989i
$151$		−	16.2206i		−	1.32002i	−0.751258	−	0.660009i	$-0.770553\pi$
$151$		−	16.2206i		−	1.32002i	0.751258	−	0.660009i	$-0.229447\pi$
$152$	−4.33926			−0.351960
$153$	−5.77569	−	1.09541i	−0.466937	−	0.0885586i
$154$	13.3341			1.07449
$155$		−	7.21615i		−	0.579615i
$156$	24.3106	−	24.3106i	1.94640	−	1.94640i
$157$	−8.52619			−0.680464			−0.340232	−	0.940341i	$-0.610506\pi$
$157$	−8.52619			−0.680464			−0.340232	+	0.940341i	$0.610506\pi$
$158$	8.96892	−	8.96892i	0.713529	−	0.713529i
$159$	−2.40787	−	2.40787i	−0.190957	−	0.190957i
$160$	2.38723	+	2.38723i	0.188727	+	0.188727i
$161$			0.231207i			0.0182216i
$162$			6.75760i			0.530927i
$163$	−10.9321	−	10.9321i	−0.856267	−	0.856267i	0.134629	−	0.990896i	$-0.457016\pi$
$163$	−10.9321	−	10.9321i	−0.856267	−	0.856267i	−0.990896	+	0.134629i	$0.957016\pi$
$164$	19.3977	+	19.3977i	1.51471	+	1.51471i
$165$	2.91592	−	2.91592i	0.227004	−	0.227004i
$166$	9.00646			0.699037
$167$	−2.59558	+	2.59558i	−0.200852	+	0.200852i	−0.800365	−	0.599513i	$-0.795361\pi$
$167$	−2.59558	+	2.59558i	−0.200852	+	0.200852i	0.599513	+	0.800365i	$0.295361\pi$
$168$			11.7669i			0.907836i
$169$	27.3891			2.10686
$170$	−8.56111	+	5.83144i	−0.656607	+	0.447251i
$171$	1.06530			0.0814653
$172$		−	11.8485i		−	0.903441i
$173$	−6.46394	+	6.46394i	−0.491444	+	0.491444i	−0.908761	−	0.417317i	$-0.862970\pi$
$173$	−6.46394	+	6.46394i	−0.491444	+	0.491444i	0.417317	+	0.908761i	$0.362970\pi$
$174$	−27.7487			−2.10363
$175$	1.14187	−	1.14187i	0.0863173	−	0.0863173i
$176$	−13.8679	−	13.8679i	−1.04533	−	1.04533i
$177$	−11.2509	−	11.2509i	−0.845669	−	0.845669i
$178$		−	26.6067i		−	1.99426i
$179$			8.76138i			0.654857i	0.944876	+	0.327428i	$0.106182\pi$
$179$			8.76138i			0.654857i	−0.944876	+	0.327428i	$0.893818\pi$
$180$	−4.34694	−	4.34694i	−0.324002	−	0.324002i
$181$	3.44161	+	3.44161i	0.255813	+	0.255813i	0.823349	−	0.567536i	$-0.192103\pi$
$181$	3.44161	+	3.44161i	0.255813	+	0.255813i	−0.567536	+	0.823349i	$0.692103\pi$
$182$	−18.2314	+	18.2314i	−1.35140	+	1.35140i
$183$	−0.582285			−0.0430437
$184$	0.587964	−	0.587964i	0.0433453	−	0.0433453i
$185$			0.621115i			0.0456653i
$186$	−22.7463			−1.66784
$187$	11.2000	−	7.62890i	0.819022	−	0.557881i
$188$	51.4418			3.75178
$189$		−	8.96715i		−	0.652264i
$190$	1.32732	−	1.32732i	0.0962937	−	0.0962937i
$191$	11.2751			0.815838			0.407919	−	0.913018i	$-0.366255\pi$
$191$	11.2751			0.815838			0.407919	+	0.913018i	$0.366255\pi$
$192$	−3.06313	+	3.06313i	−0.221062	+	0.221062i
$193$	3.23976	+	3.23976i	0.233203	+	0.233203i	0.814028	−	0.580825i	$-0.197270\pi$
$193$	3.23976	+	3.23976i	0.233203	+	0.233203i	−0.580825	+	0.814028i	$0.697270\pi$
$194$	−12.3797	−	12.3797i	−0.888809	−	0.888809i
$195$			7.97379i			0.571015i
$196$			18.9380i			1.35271i
$197$	−9.36781	−	9.36781i	−0.667429	−	0.667429i	0.289691	−	0.957120i	$-0.406447\pi$
$197$	−9.36781	−	9.36781i	−0.667429	−	0.667429i	−0.957120	+	0.289691i	$0.906447\pi$
$198$	8.32470	+	8.32470i	0.591610	+	0.591610i
$199$	−1.86562	+	1.86562i	−0.132251	+	0.132251i	−0.770133	−	0.637883i	$-0.779810\pi$
$199$	−1.86562	+	1.86562i	−0.132251	+	0.132251i	0.637883	+	0.770133i	$0.279810\pi$
$200$	−5.80761			−0.410660
$201$	−1.61190	+	1.61190i	−0.113695	+	0.113695i
$202$		−	1.70691i		−	0.120098i
$203$	14.2158			0.997751
$204$	12.5569	+	18.4347i	0.879157	+	1.29069i
$205$	−6.36239			−0.444369
$206$		−	0.393062i		−	0.0273860i
$207$	−0.144347	+	0.144347i	−0.0100328	+	0.0100328i
$208$	37.9227			2.62946
$209$	−1.73644	+	1.73644i	−0.120112	+	0.120112i
$210$	−3.59933	−	3.59933i	−0.248377	−	0.248377i
$211$	5.04513	+	5.04513i	0.347321	+	0.347321i	0.859111	−	0.511790i	$-0.171017\pi$
$211$	5.04513	+	5.04513i	0.347321	+	0.347321i	−0.511790	+	0.859111i	$0.671017\pi$
$212$		−	11.7020i		−	0.803699i
$213$		−	5.34165i		−	0.366004i
$214$	31.9145	+	31.9145i	2.18163	+	2.18163i
$215$	1.94314	+	1.94314i	0.132521	+	0.132521i
$216$	−22.8037	+	22.8037i	−1.55159	+	1.55159i
$217$	11.6530			0.791057
$218$	−10.3251	+	10.3251i	−0.699304	+	0.699304i
$219$		−	1.51974i		−	0.102694i
$220$	14.1711			0.955416
$221$	−4.88265	+	25.7444i	−0.328443	+	1.73176i
$222$	1.95784			0.131402
$223$			12.1709i			0.815025i	0.913200	+	0.407512i	$0.133604\pi$
$223$			12.1709i			0.815025i	−0.913200	+	0.407512i	$0.866396\pi$
$224$	−3.85502	+	3.85502i	−0.257575	+	0.257575i
$225$	1.42578			0.0950521
$226$	16.5161	−	16.5161i	1.09863	−	1.09863i
$227$	−0.590883	−	0.590883i	−0.0392183	−	0.0392183i	0.687226	−	0.726444i	$-0.258828\pi$
$227$	−0.590883	−	0.590883i	−0.0392183	−	0.0392183i	−0.726444	+	0.687226i	$0.758828\pi$
$228$	−2.85812	−	2.85812i	−0.189284	−	0.189284i
$229$		−	6.13420i		−	0.405360i	−0.979245	−	0.202680i	$-0.935035\pi$
$229$		−	6.13420i		−	0.405360i	0.979245	−	0.202680i	$-0.0649651\pi$
$230$			0.359700i			0.0237179i
$231$	4.70877	+	4.70877i	0.309814	+	0.309814i
$232$	−36.1511	−	36.1511i	−2.37343	−	2.37343i
$233$	−11.9056	+	11.9056i	−0.779962	+	0.779962i	−0.979824	−	0.199862i	$-0.935951\pi$
$233$	−11.9056	+	11.9056i	−0.779962	+	0.779962i	0.199862	+	0.979824i	$0.435951\pi$
$234$	−22.7645			−1.48816
$235$	−8.43638	+	8.43638i	−0.550329	+	0.550329i
$236$		−	54.6783i		−	3.55925i
$237$	6.33455			0.411473
$238$	−9.41689	−	13.8249i	−0.610407	−	0.896135i
$239$	6.95301			0.449753			0.224876	−	0.974387i	$-0.427802\pi$
$239$	6.95301			0.449753			0.224876	+	0.974387i	$0.427802\pi$
$240$			7.48685i			0.483274i
$241$	−21.7234	+	21.7234i	−1.39933	+	1.39933i	−0.597335	+	0.801992i	$0.703774\pi$
$241$	−21.7234	+	21.7234i	−1.39933	+	1.39933i	−0.801992	+	0.597335i	$0.796226\pi$
$242$	0.496655			0.0319262
$243$	9.39318	−	9.39318i	0.602573	−	0.602573i
$244$	−1.41492	−	1.41492i	−0.0905812	−	0.0905812i
$245$	−3.10580	−	3.10580i	−0.198422	−	0.198422i
$246$			20.0551i			1.27867i
$247$		−	4.74843i		−	0.302135i
$248$	−29.6339	−	29.6339i	−1.88175	−	1.88175i
$249$	3.18053	+	3.18053i	0.201558	+	0.201558i
$250$	1.77647	−	1.77647i	0.112354	−	0.112354i
$251$	22.5294			1.42204			0.711021	−	0.703171i	$-0.248233\pi$
$251$	22.5294			1.42204			0.711021	+	0.703171i	$0.248233\pi$
$252$	7.01964	−	7.01964i	0.442196	−	0.442196i
$253$		−	0.470573i		−	0.0295846i
$254$	−38.1359			−2.39286
$255$	−5.08257	−	0.963953i	−0.318283	−	0.0603651i
$256$	−31.8499			−1.99062
$257$		−	1.90476i		−	0.118816i	−0.998234	−	0.0594079i	$-0.981079\pi$
$257$		−	1.90476i		−	0.118816i	0.998234	−	0.0594079i	$-0.0189212\pi$
$258$	6.12503	−	6.12503i	0.381328	−	0.381328i
$259$	−1.00301			−0.0623238
$260$	−19.3759	+	19.3759i	−1.20164	+	1.20164i
$261$	8.87516	+	8.87516i	0.549359	+	0.549359i
$262$	3.52186	+	3.52186i	0.217581	+	0.217581i
$263$		−	7.80192i		−	0.481087i	−0.970638	−	0.240543i	$-0.922674\pi$
$263$		−	7.80192i		−	0.481087i	0.970638	−	0.240543i	$-0.0773256\pi$
$264$		−	23.9491i		−	1.47396i
$265$	1.91912	+	1.91912i	0.117890	+	0.117890i
$266$	2.14342	+	2.14342i	0.131421	+	0.131421i
$267$	9.39587	−	9.39587i	0.575018	−	0.575018i
$268$	−7.83369			−0.478519
$269$	9.71848	−	9.71848i	0.592546	−	0.592546i	−0.345772	−	0.938318i	$-0.612383\pi$
$269$	9.71848	−	9.71848i	0.592546	−	0.592546i	0.938318	+	0.345772i	$0.112383\pi$
$270$		−	13.9507i		−	0.849010i
$271$	−12.4855			−0.758438			−0.379219	−	0.925307i	$-0.623807\pi$
$271$	−12.4855			−0.758438			−0.379219	+	0.925307i	$0.623807\pi$
$272$	−4.58448	+	24.1723i	−0.277975	+	1.46566i
$273$	−12.8765			−0.779319
$274$			49.2633i			2.97611i
$275$	−2.32404	+	2.32404i	−0.140145	+	0.140145i
$276$	0.774544			0.0466221
$277$	−18.9930	+	18.9930i	−1.14118	+	1.14118i	−0.152944	+	0.988235i	$0.548875\pi$
$277$	−18.9930	+	18.9930i	−1.14118	+	1.14118i	−0.988235	+	0.152944i	$0.951125\pi$
$278$	−6.41552	−	6.41552i	−0.384777	−	0.384777i
$279$	7.27518	+	7.27518i	0.435553	+	0.435553i
$280$		−	9.37841i		−	0.560467i
$281$		−	15.5290i		−	0.926385i	−0.886258	−	0.463193i	$-0.846704\pi$
$281$		−	15.5290i		−	0.926385i	0.886258	−	0.463193i	$-0.153296\pi$
$282$	26.5926	+	26.5926i	1.58357	+	1.58357i
$283$	−7.38186	−	7.38186i	−0.438806	−	0.438806i	0.452804	−	0.891610i	$-0.350424\pi$
$283$	−7.38186	−	7.38186i	−0.438806	−	0.438806i	−0.891610	+	0.452804i	$0.850424\pi$
$284$	12.9800	−	12.9800i	0.770219	−	0.770219i
$285$	0.937454			0.0555300
$286$	37.1063	−	37.1063i	2.19414	−	2.19414i
$287$		−	10.2743i		−	0.606473i
$288$	−4.81352			−0.283640
$289$	−15.8195	−	6.22450i	−0.930557	−	0.366147i
$290$	22.1162			1.29871
$291$		−	8.74348i		−	0.512552i
$292$	3.69289	−	3.69289i	0.216110	−	0.216110i
$293$	7.10645			0.415163			0.207581	−	0.978218i	$-0.433441\pi$
$293$	7.10645			0.415163			0.207581	+	0.978218i	$0.433441\pi$
$294$	−9.78989	+	9.78989i	−0.570958	+	0.570958i
$295$	8.96715	+	8.96715i	0.522087	+	0.522087i
$296$	2.55067	+	2.55067i	0.148255	+	0.148255i
$297$			18.2508i			1.05902i
$298$		−	3.17560i		−	0.183958i
$299$	0.643407	+	0.643407i	0.0372092	+	0.0372092i
$300$	−3.82528	−	3.82528i	−0.220852	−	0.220852i
$301$	−3.13787	+	3.13787i	−0.180864	+	0.180864i
$302$	40.7512			2.34497
$303$	0.602777	−	0.602777i	0.0346286	−	0.0346286i
$304$		−	4.45845i		−	0.255710i
$305$	0.464091			0.0265738
$306$	2.75200	−	14.5103i	0.157321	−	0.829498i
$307$	4.80512			0.274243			0.137121	−	0.990554i	$-0.456215\pi$
$307$	4.80512			0.274243			0.137121	+	0.990554i	$0.456215\pi$
$308$			22.8842i			1.30395i
$309$	0.138806	−	0.138806i	0.00789637	−	0.00789637i
$310$	18.1292			1.02967
$311$	−5.67759	+	5.67759i	−0.321947	+	0.321947i	−0.849514	−	0.527567i	$-0.823104\pi$
$311$	−5.67759	+	5.67759i	−0.321947	+	0.321947i	0.527567	+	0.849514i	$0.323104\pi$
$312$	32.7452	+	32.7452i	1.85383	+	1.85383i
$313$	15.6285	+	15.6285i	0.883374	+	0.883374i	0.993876	−	0.110502i	$-0.0352458\pi$
$313$	15.6285	+	15.6285i	0.883374	+	0.883374i	−0.110502	+	0.993876i	$0.535246\pi$
$314$		−	21.4204i		−	1.20882i
$315$			2.30242i			0.129727i
$316$	15.3927	+	15.3927i	0.865905	+	0.865905i
$317$	−11.2888	−	11.2888i	−0.634041	−	0.634041i	0.315038	−	0.949079i	$-0.397983\pi$
$317$	−11.2888	−	11.2888i	−0.634041	−	0.634041i	−0.949079	+	0.315038i	$0.897983\pi$
$318$	6.04931	−	6.04931i	0.339228	−	0.339228i
$319$	−28.9332			−1.61995
$320$	2.44136	−	2.44136i	0.136476	−	0.136476i
$321$			22.5405i			1.25809i
$322$	−0.580861			−0.0323701
$323$	3.02669	+	0.574039i	0.168410	+	0.0319404i
$324$	−11.5975			−0.644308
$325$		−	6.35524i		−	0.352526i
$326$	27.4647	−	27.4647i	1.52113	−	1.52113i
$327$	−7.29238			−0.403270
$328$	−26.1278	+	26.1278i	−1.44267	+	1.44267i
$329$	−13.6235	−	13.6235i	−0.751086	−	0.751086i
$330$	7.32568	+	7.32568i	0.403265	+	0.403265i
$331$		−	3.87911i		−	0.213215i	−0.994301	−	0.106608i	$-0.966001\pi$
$331$		−	3.87911i		−	0.213215i	0.994301	−	0.106608i	$-0.0339989\pi$
$332$			15.4571i			0.848317i
$333$	−0.626196	−	0.626196i	−0.0343153	−	0.0343153i
$334$	−6.52088	−	6.52088i	−0.356807	−	0.356807i
$335$	1.28471	−	1.28471i	0.0701914	−	0.0701914i
$336$	−12.0901			−0.659571
$337$	−17.2431	+	17.2431i	−0.939290	+	0.939290i	−0.998260	−	0.0589698i	$-0.981218\pi$
$337$	−17.2431	+	17.2431i	−0.939290	+	0.939290i	0.0589698	+	0.998260i	$0.481218\pi$
$338$			68.8098i			3.74276i
$339$	11.6649			0.633553
$340$	−10.0080	−	14.6928i	−0.542762	−	0.796827i
$341$	−23.7172			−1.28436
$342$			2.67635i			0.144720i
$343$	13.0085	−	13.0085i	0.702392	−	0.702392i
$344$	15.9594			0.860473
$345$	−0.127024	+	0.127024i	−0.00683874	+	0.00683874i
$346$	−16.2394	−	16.2394i	−0.873034	−	0.873034i
$347$	7.51698	+	7.51698i	0.403532	+	0.403532i	0.879476	−	0.475943i	$-0.157893\pi$
$347$	7.51698	+	7.51698i	0.403532	+	0.403532i	−0.475943	+	0.879476i	$0.657893\pi$
$348$		−	47.6229i		−	2.55286i
$349$		−	11.5579i		−	0.618682i	−0.950951	−	0.309341i	$-0.899892\pi$
$349$		−	11.5579i		−	0.618682i	0.950951	−	0.309341i	$-0.100108\pi$
$350$	2.86872	+	2.86872i	0.153340	+	0.153340i
$351$	−24.9540	−	24.9540i	−1.33194	−	1.33194i
$352$	7.84609	−	7.84609i	0.418198	−	0.418198i
$353$	−11.3682			−0.605070			−0.302535	−	0.953138i	$-0.597833\pi$
$353$	−11.3682			−0.605070			−0.302535	+	0.953138i	$0.597833\pi$
$354$	28.2656	−	28.2656i	1.50230	−	1.50230i
$355$			4.25738i			0.225958i
$356$	45.6631			2.42014
$357$	1.55664	−	8.20758i	0.0823861	−	0.434391i
$358$	−22.0113			−1.16333
$359$			32.1310i			1.69581i	0.530147	+	0.847906i	$0.322137\pi$
$359$			32.1310i			1.69581i	−0.530147	+	0.847906i	$0.677863\pi$
$360$	5.85512	−	5.85512i	0.308592	−	0.308592i
$361$	18.4417			0.970618
$362$	−8.64637	+	8.64637i	−0.454443	+	0.454443i
$363$	0.175388	+	0.175388i	0.00920548	+	0.00920548i
$364$	−31.2892	−	31.2892i	−1.64000	−	1.64000i
$365$			1.21126i			0.0634001i
$366$		−	1.46288i		−	0.0764657i
$367$	−13.6155	−	13.6155i	−0.710723	−	0.710723i	0.255964	−	0.966686i	$-0.417607\pi$
$367$	−13.6155	−	13.6155i	−0.710723	−	0.710723i	−0.966686	+	0.255964i	$0.917607\pi$
$368$	0.604116	+	0.604116i	0.0314917	+	0.0314917i
$369$	6.41443	−	6.41443i	0.333922	−	0.333922i
$370$	−1.56043			−0.0811229
$371$	−3.09908	+	3.09908i	−0.160896	+	0.160896i
$372$		−	39.0376i		−	2.02401i
$373$	−20.3136			−1.05180			−0.525900	−	0.850547i	$-0.676271\pi$
$373$	−20.3136			−1.05180			−0.525900	+	0.850547i	$0.676271\pi$
$374$	19.1661	+	28.1377i	0.991056	+	1.45497i
$375$	1.25468			0.0647913
$376$			69.2897i			3.57334i
$377$	39.5599	−	39.5599i	2.03744	−	2.03744i
$378$	22.5282			1.15873
$379$	24.2540	−	24.2540i	1.24585	−	1.24585i	0.288308	−	0.957538i	$-0.406907\pi$
$379$	24.2540	−	24.2540i	1.24585	−	1.24585i	0.957538	−	0.288308i	$-0.0930928\pi$
$380$	2.27797	+	2.27797i	0.116857	+	0.116857i
$381$	−13.4673	−	13.4673i	−0.689948	−	0.689948i
$382$			28.3265i			1.44931i
$383$			21.3225i			1.08953i	0.838589	+	0.544764i	$0.183381\pi$
$383$			21.3225i			1.08953i	−0.838589	+	0.544764i	$0.816619\pi$
$384$	−13.6859	−	13.6859i	−0.698407	−	0.698407i
$385$	−3.75297	−	3.75297i	−0.191269	−	0.191269i
$386$	−8.13925	+	8.13925i	−0.414277	+	0.414277i
$387$	−3.91807			−0.199166
$388$	21.2463	−	21.2463i	1.07862	−	1.07862i
$389$		−	11.7682i		−	0.596672i	−0.954461	−	0.298336i	$-0.903568\pi$
$389$		−	11.7682i		−	0.596672i	0.954461	−	0.298336i	$-0.0964316\pi$
$390$	−20.0326			−1.01439
$391$	−0.487895	+	0.332332i	−0.0246739	+	0.0168067i
$392$	−25.5086			−1.28838
$393$			2.48741i			0.125473i
$394$	23.5348	−	23.5348i	1.18567	−	1.18567i
$395$	−5.04874			−0.254030
$396$	−14.2870	+	14.2870i	−0.717950	+	0.717950i
$397$	2.37514	+	2.37514i	0.119205	+	0.119205i	0.764193	−	0.644988i	$-0.223138\pi$
$397$	2.37514	+	2.37514i	0.119205	+	0.119205i	−0.644988	+	0.764193i	$0.723138\pi$
$398$	−4.68701	−	4.68701i	−0.234939	−	0.234939i
$399$			1.51385i			0.0757871i
$400$		−	5.96715i		−	0.298357i
$401$	−1.83450	−	1.83450i	−0.0916105	−	0.0916105i	0.659816	−	0.751427i	$-0.270634\pi$
$401$	−1.83450	−	1.83450i	−0.0916105	−	0.0916105i	−0.751427	+	0.659816i	$0.770634\pi$
$402$	−4.04959	−	4.04959i	−0.201975	−	0.201975i
$403$	32.4282	−	32.4282i	1.61536	−	1.61536i
$404$	2.92944			0.145745
$405$	1.90198	−	1.90198i	0.0945100	−	0.0945100i
$406$			35.7143i			1.77247i
$407$	2.04141			0.101189
$408$	−24.8307	+	16.9135i	−1.22930	+	0.837344i
$409$	−30.8364			−1.52476			−0.762381	−	0.647129i	$-0.775970\pi$
$409$	−30.8364			−1.52476			−0.762381	+	0.647129i	$0.775970\pi$
$410$		−	15.9843i		−	0.789406i
$411$	−17.3968	+	17.3968i	−0.858120	+	0.858120i
$412$	0.674582			0.0332343
$413$	−14.4806	+	14.4806i	−0.712543	+	0.712543i
$414$	−0.362642	−	0.362642i	−0.0178229	−	0.0178229i
$415$	−2.53494	−	2.53494i	−0.124435	−	0.124435i
$416$			21.4557i			1.05195i
$417$		−	4.53114i		−	0.221891i
$418$	−4.36248	−	4.36248i	−0.213376	−	0.213376i
$419$	13.1997	+	13.1997i	0.644849	+	0.644849i	0.951744	−	0.306894i	$-0.0992898\pi$
$419$	13.1997	+	13.1997i	0.644849	+	0.644849i	−0.306894	+	0.951744i	$0.599290\pi$
$420$	6.17724	−	6.17724i	0.301419	−	0.301419i
$421$	−29.5695			−1.44113			−0.720565	−	0.693388i	$-0.756117\pi$
$421$	−29.5695			−1.44113			−0.720565	+	0.693388i	$0.756117\pi$
$422$	−12.6749	+	12.6749i	−0.617004	+	0.617004i
$423$		−	17.0108i		−	0.827092i
$424$	15.7621			0.765475
$425$	4.05089	+	0.768287i	0.196497	+	0.0372674i
$426$	13.4198			0.650193
$427$			0.749436i			0.0362678i
$428$	−54.7724	+	54.7724i	−2.64752	+	2.64752i
$429$	26.2074			1.26530
$430$	−4.88175	+	4.88175i	−0.235419	+	0.235419i
$431$	11.5583	+	11.5583i	0.556744	+	0.556744i	0.928379	−	0.371635i	$-0.121203\pi$
$431$	11.5583	+	11.5583i	0.556744	+	0.556744i	−0.371635	+	0.928379i	$0.621203\pi$
$432$	−23.4301	−	23.4301i	−1.12728	−	1.12728i
$433$			14.3256i			0.688446i	0.938888	+	0.344223i	$0.111858\pi$
$433$			14.3256i			0.688446i	−0.938888	+	0.344223i	$0.888142\pi$
$434$			29.2758i			1.40529i
$435$	7.81009	+	7.81009i	0.374465	+	0.374465i
$436$	−17.7202	−	17.7202i	−0.848641	−	0.848641i
$437$	0.0756434	−	0.0756434i	0.00361851	−	0.00361851i
$438$	3.81805			0.182433
$439$	−21.5167	+	21.5167i	−1.02694	+	1.02694i	−0.0273099	+	0.999627i	$0.508694\pi$
$439$	−21.5167	+	21.5167i	−1.02694	+	1.02694i	−0.999627	+	0.0273099i	$0.991306\pi$
$440$			19.0878i			0.909975i
$441$	6.26241			0.298210
$442$	−64.6778	−	12.2667i	−3.07641	−	0.583468i
$443$	26.5036			1.25922			0.629612	−	0.776909i	$-0.283214\pi$
$443$	26.5036			1.25922			0.629612	+	0.776909i	$0.283214\pi$
$444$			3.36008i			0.159463i
$445$	−7.48867	+	7.48867i	−0.354997	+	0.354997i
$446$	−30.5770			−1.44786
$447$	1.12143	−	1.12143i	0.0530418	−	0.0530418i
$448$	3.94243	+	3.94243i	0.186262	+	0.186262i
$449$	11.1999	+	11.1999i	0.528556	+	0.528556i	0.920142	−	0.391585i	$-0.128073\pi$
$449$	11.1999	+	11.1999i	0.528556	+	0.528556i	−0.391585	+	0.920142i	$0.628073\pi$
$450$			3.58200i			0.168857i
$451$			20.9112i			0.984669i
$452$	28.3453	+	28.3453i	1.33325	+	1.33325i
$453$	14.3908	+	14.3908i	0.676140	+	0.676140i
$454$	1.48448	−	1.48448i	0.0696700	−	0.0696700i
$455$	10.2628			0.481126
$456$	3.84975	−	3.84975i	0.180281	−	0.180281i
$457$		−	4.25348i		−	0.198969i	−0.995039	−	0.0994847i	$-0.968281\pi$
$457$		−	4.25348i		−	0.198969i	0.995039	−	0.0994847i	$-0.0317194\pi$
$458$	15.4110			0.720108
$459$	18.9226	−	12.8892i	0.883231	−	0.601617i
$460$	−0.617325			−0.0287829
$461$		−	23.9740i		−	1.11658i	−0.829646	−	0.558290i	$-0.811458\pi$
$461$		−	23.9740i		−	1.11658i	0.829646	−	0.558290i	$-0.188542\pi$
$462$	−11.8299	+	11.8299i	−0.550375	+	0.550375i
$463$	23.0127			1.06949			0.534746	−	0.845013i	$-0.320407\pi$
$463$	23.0127			1.06949			0.534746	+	0.845013i	$0.320407\pi$
$464$	37.1441	−	37.1441i	1.72437	−	1.72437i
$465$	6.40211	+	6.40211i	0.296891	+	0.296891i
$466$	−29.9105	−	29.9105i	−1.38558	−	1.38558i
$467$		−	21.7845i		−	1.00807i	−0.863684	−	0.504033i	$-0.831849\pi$
$467$		−	21.7845i		−	1.00807i	0.863684	−	0.504033i	$-0.168151\pi$
$468$		−	39.0688i		−	1.80596i
$469$	2.07462	+	2.07462i	0.0957969	+	0.0957969i
$470$	−21.1947	−	21.1947i	−0.977640	−	0.977640i
$471$	7.56437	−	7.56437i	0.348548	−	0.348548i
$472$	73.6490			3.38997
$473$	6.38649	−	6.38649i	0.293651	−	0.293651i
$474$			15.9143i			0.730968i
$475$	−0.747167			−0.0342824
$476$	23.7266	−	16.1615i	1.08751	−	0.740760i
$477$	−3.86963			−0.177178
$478$			17.4681i			0.798971i
$479$	−23.2853	+	23.2853i	−1.06393	+	1.06393i	−0.0661200	+	0.997812i	$0.521062\pi$
$479$	−23.2853	+	23.2853i	−1.06393	+	1.06393i	−0.997812	+	0.0661200i	$0.978938\pi$
$480$	−4.23587			−0.193340
$481$	−2.79119	+	2.79119i	−0.127267	+	0.127267i
$482$	−54.5758	−	54.5758i	−2.48586	−	2.48586i
$483$	−0.205125	−	0.205125i	−0.00933349	−	0.00933349i
$484$			0.852369i			0.0387441i
$485$			6.96870i			0.316433i
$486$	23.5985	+	23.5985i	1.07045	+	1.07045i
$487$	−13.1864	−	13.1864i	−0.597535	−	0.597535i	0.342121	−	0.939656i	$-0.388855\pi$
$487$	−13.1864	−	13.1864i	−0.597535	−	0.597535i	−0.939656	+	0.342121i	$0.888855\pi$
$488$	1.90584	−	1.90584i	0.0862731	−	0.0862731i
$489$	19.3977			0.877195
$490$	7.80271	−	7.80271i	0.352491	−	0.352491i
$491$		−	3.97306i		−	0.179302i	−0.995973	−	0.0896508i	$-0.971425\pi$
$491$		−	3.97306i		−	0.179302i	0.995973	−	0.0896508i	$-0.0285751\pi$
$492$	−34.4190			−1.55173
$493$	20.4335	+	29.9983i	0.920277	+	1.35106i
$494$	11.9295			0.536733
$495$		−	4.68610i		−	0.210624i
$496$	30.4479	−	30.4479i	1.36715	−	1.36715i
$497$	−6.87503			−0.308387
$498$	−7.99046	+	7.99046i	−0.358061	+	0.358061i
$499$	−24.1326	−	24.1326i	−1.08032	−	1.08032i	−0.996479	−	0.0838426i	$-0.973281\pi$
$499$	−24.1326	−	24.1326i	−1.08032	−	1.08032i	−0.0838426	−	0.996479i	$-0.526719\pi$
$500$	3.04881	+	3.04881i	0.136347	+	0.136347i
$501$		−	4.60555i		−	0.205761i
$502$			56.6007i			2.52621i
$503$	27.8677	+	27.8677i	1.24256	+	1.24256i	0.958935	+	0.283626i	$0.0915375\pi$
$503$	27.8677	+	27.8677i	1.24256	+	1.24256i	0.283626	+	0.958935i	$0.408463\pi$
$504$	9.45513	+	9.45513i	0.421165	+	0.421165i
$505$	−0.480423	+	0.480423i	−0.0213785	+	0.0213785i
$506$	1.18222			0.0525561
$507$	−24.2994	+	24.2994i	−1.07917	+	1.07917i
$508$		−	65.4496i		−	2.90386i
$509$	8.87274			0.393277			0.196639	−	0.980476i	$-0.436997\pi$
$509$	8.87274			0.393277			0.196639	+	0.980476i	$0.436997\pi$
$510$	2.42174	−	12.7690i	0.107237	−	0.565419i
$511$	−1.95600			−0.0865282
$512$		−	49.1643i		−	2.17278i
$513$	−2.93376	+	2.93376i	−0.129529	+	0.129529i
$514$	4.78534			0.211072
$515$	−0.110630	+	0.110630i	−0.00487496	+	0.00487496i
$516$	10.5119	+	10.5119i	0.462761	+	0.462761i
$517$	27.7277	+	27.7277i	1.21946	+	1.21946i
$518$		−	2.51986i		−	0.110716i
$519$		−	11.4695i		−	0.503455i
$520$	−26.0985	−	26.0985i	−1.14449	−	1.14449i
$521$	12.4387	+	12.4387i	0.544948	+	0.544948i	0.924975	−	0.380027i	$-0.124085\pi$
$521$	12.4387	+	12.4387i	0.544948	+	0.544948i	−0.380027	+	0.924975i	$0.624085\pi$
$522$	−22.2971	+	22.2971i	−0.975918	+	0.975918i
$523$	−20.1681			−0.881892			−0.440946	−	0.897534i	$-0.645357\pi$
$523$	−20.1681			−0.881892			−0.440946	+	0.897534i	$0.645357\pi$
$524$	−6.04428	+	6.04428i	−0.264046	+	0.264046i
$525$			2.02612i			0.0884270i
$526$	19.6008			0.854635
$527$	16.7498	+	24.5903i	0.729632	+	1.07117i
$528$	24.6069			1.07088
$529$		−	22.9795i		−	0.999109i
$530$	−4.82140	+	4.82140i	−0.209428	+	0.209428i
$531$	−18.0810			−0.784648
$532$	−3.67858	+	3.67858i	−0.159487	+	0.159487i
$533$	−28.5915	−	28.5915i	−1.23844	−	1.23844i
$534$	23.6053	+	23.6053i	1.02150	+	1.02150i
$535$		−	17.9652i		−	0.776702i
$536$		−	10.5516i		−	0.455760i
$537$	−7.77303	−	7.77303i	−0.335431	−	0.335431i
$538$	24.4158	+	24.4158i	1.05264	+	1.05264i
$539$	−10.2078	+	10.2078i	−0.439681	+	0.439681i
$540$	23.9424			1.03032
$541$	30.2202	−	30.2202i	1.29927	−	1.29927i	0.370391	−	0.928876i	$-0.379224\pi$
$541$	30.2202	−	30.2202i	1.29927	−	1.29927i	0.928876	−	0.370391i	$-0.120776\pi$
$542$		−	31.3673i		−	1.34734i
$543$	−6.10674			−0.262065
$544$	−13.6761	−	2.59378i	−0.586356	−	0.111208i
$545$	5.81215			0.248965
$546$		−	32.3496i		−	1.38443i
$547$	10.0510	−	10.0510i	0.429751	−	0.429751i	−0.458792	−	0.888544i	$-0.651718\pi$
$547$	10.0510	−	10.0510i	0.429751	−	0.429751i	0.888544	+	0.458792i	$0.151718\pi$
$548$	−84.5468			−3.61166
$549$	−0.467887	+	0.467887i	−0.0199689	+	0.0199689i
$550$	−5.83869	−	5.83869i	−0.248963	−	0.248963i
$551$	−4.65094	−	4.65094i	−0.198137	−	0.198137i
$552$			1.04327i			0.0444047i
$553$		−	8.15295i		−	0.346699i
$554$	−47.7162	−	47.7162i	−2.02727	−	2.02727i
$555$	−0.551049	−	0.551049i	−0.0233907	−	0.0233907i
$556$	11.0105	−	11.0105i	0.466947	−	0.466947i
$557$	−4.00971			−0.169897			−0.0849484	−	0.996385i	$-0.527073\pi$
$557$	−4.00971			−0.169897			−0.0849484	+	0.996385i	$0.527073\pi$
$558$	−18.2775	+	18.2775i	−0.773746	+	0.773746i
$559$			17.4643i			0.738661i
$560$	9.63604			0.407197
$561$	−3.16821	+	16.7048i	−0.133762	+	0.705278i
$562$	39.0137			1.64569
$563$			5.66772i			0.238866i	0.992842	+	0.119433i	$0.0381077\pi$
$563$			5.66772i			0.238866i	−0.992842	+	0.119433i	$0.961892\pi$
$564$	−45.6388	+	45.6388i	−1.92174	+	1.92174i
$565$	−9.29716			−0.391134
$566$	18.5455	−	18.5455i	0.779524	−	0.779524i
$567$	3.07141	+	3.07141i	0.128987	+	0.128987i
$568$	17.4834	+	17.4834i	0.733586	+	0.733586i
$569$			0.249161i			0.0104454i	0.999986	+	0.00522269i	$0.00166244\pi$
$569$			0.249161i			0.0104454i	−0.999986	+	0.00522269i	$0.998338\pi$
$570$			2.35517i			0.0986472i
$571$	24.1579	+	24.1579i	1.01098	+	1.01098i	0.999939	+	0.0110385i	$0.00351375\pi$
$571$	24.1579	+	24.1579i	1.01098	+	1.01098i	0.0110385	+	0.999939i	$0.496486\pi$
$572$	63.6826	+	63.6826i	2.66270	+	2.66270i
$573$	−10.0032	+	10.0032i	−0.417889	+	0.417889i
$574$	25.8122			1.07738
$575$	0.101240	−	0.101240i	0.00422201	−	0.00422201i
$576$			4.92267i			0.205111i
$577$	28.3587			1.18059			0.590295	−	0.807188i	$-0.299011\pi$
$577$	28.3587			1.18059			0.590295	+	0.807188i	$0.299011\pi$
$578$	15.6378	−	39.7433i	0.650448	−	1.65310i
$579$	−5.74857			−0.238902
$580$			37.9563i			1.57605i
$581$	4.09354	−	4.09354i	0.169829	−	0.169829i
$582$	21.9663			0.910532
$583$	6.30753	−	6.30753i	0.261231	−	0.261231i
$584$	4.97415	+	4.97415i	0.205832	+	0.205832i
$585$	6.40723	+	6.40723i	0.264906	+	0.264906i
$586$			17.8535i			0.737523i
$587$		−	22.8461i		−	0.942960i	−0.881877	−	0.471480i	$-0.843720\pi$
$587$		−	22.8461i		−	0.942960i	0.881877	−	0.471480i	$-0.156280\pi$
$588$	−16.8016	−	16.8016i	−0.692887	−	0.692887i
$589$	−3.81249	−	3.81249i	−0.157091	−	0.157091i
$590$	−22.5282	+	22.5282i	−0.927471	+	0.927471i
$591$	16.6221			0.683742
$592$	−2.62074	+	2.62074i	−0.107712	+	0.107712i
$593$		−	10.3077i		−	0.423285i	−0.977347	−	0.211642i	$-0.932119\pi$
$593$		−	10.3077i		−	0.423285i	0.977347	−	0.211642i	$-0.0678812\pi$
$594$	−45.8514			−1.88131
$595$	−1.24067	+	6.54158i	−0.0508624	+	0.268179i
$596$	5.45004			0.223242
$597$		−	3.31033i		−	0.135483i
$598$	−1.61643	+	1.61643i	−0.0661009	+	0.0661009i
$599$	25.2157			1.03028			0.515142	−	0.857105i	$-0.327739\pi$
$599$	25.2157			1.03028			0.515142	+	0.857105i	$0.327739\pi$
$600$	5.15247	−	5.15247i	0.210349	−	0.210349i
$601$	−6.05550	−	6.05550i	−0.247009	−	0.247009i	0.572733	−	0.819742i	$-0.305883\pi$
$601$	−6.05550	−	6.05550i	−0.247009	−	0.247009i	−0.819742	+	0.572733i	$0.805883\pi$
$602$	−7.88329	−	7.88329i	−0.321299	−	0.321299i
$603$			2.59044i			0.105491i
$604$			69.9380i			2.84574i
$605$	−0.139787	−	0.139787i	−0.00568316	−	0.00568316i
$606$	1.51436	+	1.51436i	0.0615166	+	0.0615166i
$607$	6.94394	−	6.94394i	0.281846	−	0.281846i	−0.551999	−	0.833845i	$-0.686135\pi$
$607$	6.94394	−	6.94394i	0.281846	−	0.281846i	0.833845	+	0.551999i	$0.186135\pi$
$608$	2.52248			0.102300
$609$	−12.6121	+	12.6121i	−0.511069	+	0.511069i
$610$			1.16594i			0.0472074i
$611$	−75.8234			−3.06749
$612$	24.9029	+	4.72304i	1.00664	+	0.190918i
$613$	22.3926			0.904427			0.452214	−	0.891910i	$-0.350635\pi$
$613$	22.3926			0.904427			0.452214	+	0.891910i	$0.350635\pi$
$614$			12.0719i			0.487183i
$615$	5.64466	−	5.64466i	0.227615	−	0.227615i
$616$	−30.8239			−1.24193
$617$	−15.0930	+	15.0930i	−0.607620	+	0.607620i	−0.942323	−	0.334704i	$-0.891364\pi$
$617$	−15.0930	+	15.0930i	−0.607620	+	0.607620i	0.334704	+	0.942323i	$0.391364\pi$
$618$	0.348722	+	0.348722i	0.0140276	+	0.0140276i
$619$	−10.6460	−	10.6460i	−0.427900	−	0.427900i	0.460013	−	0.887912i	$-0.347845\pi$
$619$	−10.6460	−	10.6460i	−0.427900	−	0.427900i	−0.887912	+	0.460013i	$0.847845\pi$
$620$			31.1136i			1.24955i
$621$		−	0.795043i		−	0.0319040i
$622$	−14.2638	−	14.2638i	−0.571928	−	0.571928i
$623$	−12.0931	−	12.0931i	−0.484499	−	0.484499i
$624$	−33.6447	+	33.6447i	−1.34687	+	1.34687i
$625$	−1.00000			−0.0400000
$626$	−39.2635	+	39.2635i	−1.56928	+	1.56928i
$627$		−	3.08112i		−	0.123048i
$628$	36.7621			1.46697
$629$	−1.44170	−	2.11656i	−0.0574845	−	0.0843928i
$630$	−5.78438			−0.230455
$631$		−	41.6046i		−	1.65625i	−0.560540	−	0.828127i	$-0.689406\pi$
$631$		−	41.6046i		−	1.65625i	0.560540	−	0.828127i	$-0.310594\pi$
$632$	−20.7332	+	20.7332i	−0.824721	+	0.824721i
$633$	−8.95199			−0.355810
$634$	28.3608	−	28.3608i	1.12635	−	1.12635i
$635$	10.7336	+	10.7336i	0.425951	+	0.425951i
$636$	10.3820	+	10.3820i	0.411671	+	0.411671i
$637$		−	27.9139i		−	1.10599i
$638$		−	72.6890i		−	2.87779i
$639$	−4.29221	−	4.29221i	−0.169797	−	0.169797i
$640$	10.9079	+	10.9079i	0.431173	+	0.431173i
$641$	6.26768	−	6.26768i	0.247559	−	0.247559i	−0.572409	−	0.819968i	$-0.693991\pi$
$641$	6.26768	−	6.26768i	0.247559	−	0.247559i	0.819968	+	0.572409i	$0.193991\pi$
$642$	−56.6286			−2.23495
$643$	−21.2314	+	21.2314i	−0.837285	+	0.837285i	−0.988501	−	0.151216i	$-0.951681\pi$
$643$	−21.2314	+	21.2314i	−0.837285	+	0.837285i	0.151216	+	0.988501i	$0.451681\pi$
$644$		−	0.996886i		−	0.0392828i
$645$	−3.44787			−0.135760
$646$	−1.44216	+	7.60397i	−0.0567410	+	0.299174i
$647$	0.383859			0.0150911			0.00754553	−	0.999972i	$-0.497598\pi$
$647$	0.383859			0.0150911			0.00754553	+	0.999972i	$0.497598\pi$
$648$		−	15.6213i		−	0.613664i
$649$	29.4722	−	29.4722i	1.15689	−	1.15689i
$650$	15.9663			0.626250
$651$	−10.3384	+	10.3384i	−0.405195	+	0.405195i
$652$	47.1355	+	47.1355i	1.84597	+	1.84597i
$653$	1.02342	+	1.02342i	0.0400497	+	0.0400497i	0.726848	−	0.686798i	$-0.240984\pi$
$653$	1.02342	+	1.02342i	0.0400497	+	0.0400497i	−0.686798	+	0.726848i	$0.740984\pi$
$654$		−	18.3207i		−	0.716395i
$655$		−	1.98251i		−	0.0774629i
$656$	−26.8455	−	26.8455i	−1.04814	−	1.04814i
$657$	−1.22117	−	1.22117i	−0.0476422	−	0.0476422i
$658$	34.2263	−	34.2263i	1.33428	−	1.33428i
$659$	−21.8603			−0.851555			−0.425777	−	0.904828i	$-0.639999\pi$
$659$	−21.8603			−0.851555			−0.425777	+	0.904828i	$0.639999\pi$
$660$	−12.5725	+	12.5725i	−0.489383	+	0.489383i
$661$			40.5201i			1.57605i	0.615644	+	0.788024i	$0.288896\pi$
$661$			40.5201i			1.57605i	−0.615644	+	0.788024i	$0.711104\pi$
$662$	9.74551			0.378770
$663$	−18.5084	−	27.1721i	−0.718806	−	1.05528i
$664$	−20.8200			−0.807971
$665$		−	1.20656i		−	0.0467884i
$666$	1.57319	−	1.57319i	0.0609600	−	0.0609600i
$667$	1.26040			0.0488027
$668$	11.1913	−	11.1913i	0.433004	−	0.433004i
$669$	−10.7979	−	10.7979i	−0.417472	−	0.417472i
$670$	3.22759	+	3.22759i	0.124693	+	0.124693i
$671$		−	1.52532i		−	0.0588844i
$672$		−	6.84029i		−	0.263870i
$673$	−5.61265	−	5.61265i	−0.216352	−	0.216352i	0.590607	−	0.806959i	$-0.298888\pi$
$673$	−5.61265	−	5.61265i	−0.216352	−	0.216352i	−0.806959	+	0.590607i	$0.798888\pi$
$674$	−43.3198	−	43.3198i	−1.66862	−	1.66862i
$675$	−3.92652	+	3.92652i	−0.151132	+	0.151132i
$676$	−118.093			−4.54203
$677$	−1.81406	+	1.81406i	−0.0697200	+	0.0697200i	−0.741107	−	0.671387i	$-0.765699\pi$
$677$	−1.81406	+	1.81406i	−0.0697200	+	0.0697200i	0.671387	+	0.741107i	$0.265699\pi$
$678$			29.3059i			1.12549i
$679$	−11.2534			−0.431866
$680$	19.7905	−	13.4804i	0.758929	−	0.516948i
$681$	1.04845			0.0401768
$682$		−	59.5849i		−	2.28162i
$683$	−10.2987	+	10.2987i	−0.394070	+	0.394070i	−0.876135	−	0.482065i	$-0.839887\pi$
$683$	−10.2987	+	10.2987i	−0.394070	+	0.394070i	0.482065	+	0.876135i	$0.339887\pi$
$684$	−4.59321			−0.175626
$685$	13.8655	−	13.8655i	0.529775	−	0.529775i
$686$	32.6813	+	32.6813i	1.24778	+	1.24778i
$687$	5.44221	+	5.44221i	0.207633	+	0.207633i
$688$			16.3978i			0.625160i
$689$			17.2484i			0.657111i
$690$	−0.319123	−	0.319123i	−0.0121488	−	0.0121488i
$691$	30.3791	+	30.3791i	1.15567	+	1.15567i	0.985396	+	0.170278i	$0.0544665\pi$
$691$	30.3791	+	30.3791i	1.15567	+	1.15567i	0.170278	+	0.985396i	$0.445533\pi$
$692$	27.8703	−	27.8703i	1.05947	−	1.05947i
$693$	7.56734			0.287459
$694$	−18.8849	+	18.8849i	−0.716862	+	0.716862i
$695$			3.61139i			0.136988i
$696$	64.1458			2.43144
$697$	21.6810	−	14.7681i	0.821225	−	0.559381i
$698$	29.0370			1.09907
$699$		−	21.1251i		−	0.799025i
$700$	−4.92337	+	4.92337i	−0.186086	+	0.186086i
$701$	46.4002			1.75251			0.876256	−	0.481846i	$-0.160033\pi$
$701$	46.4002			1.75251			0.876256	+	0.481846i	$0.160033\pi$
$702$	62.6920	−	62.6920i	2.36616	−	2.36616i
$703$	0.328152	+	0.328152i	0.0123765	+	0.0123765i
$704$	−8.02400	−	8.02400i	−0.302416	−	0.302416i
$705$		−	14.9694i		−	0.563779i
$706$		−	28.5605i		−	1.07489i
$707$	−0.775811	−	0.775811i	−0.0291774	−	0.0291774i
$708$	48.5101	+	48.5101i	1.82312	+	1.82312i
$709$	−29.3677	+	29.3677i	−1.10293	+	1.10293i	−0.108871	+	0.994056i	$0.534724\pi$
$709$	−29.3677	+	29.3677i	−1.10293	+	1.10293i	−0.994056	+	0.108871i	$0.965276\pi$
$710$	−10.6958			−0.401408
$711$	5.09004	−	5.09004i	0.190891	−	0.190891i
$712$			61.5060i			2.30503i
$713$	1.03317			0.0386927
$714$	20.6199	+	3.91075i	0.771681	+	0.146356i
$715$	−20.8877			−0.781156
$716$		−	37.7762i		−	1.41176i
$717$	−6.16865	+	6.16865i	−0.230373	+	0.230373i
$718$	−80.7229			−3.01255
$719$	−0.455602	+	0.455602i	−0.0169911	+	0.0169911i	−0.715551	−	0.698560i	$-0.753824\pi$
$719$	−0.455602	+	0.455602i	−0.0169911	+	0.0169911i	0.698560	+	0.715551i	$0.253824\pi$
$720$	6.01596	+	6.01596i	0.224201	+	0.224201i
$721$	−0.178651	−	0.178651i	−0.00665332	−	0.00665332i
$722$			46.3313i			1.72427i
$723$		−	38.5456i		−	1.43353i
$724$	−14.8391	−	14.8391i	−0.551490	−	0.551490i
$725$	−6.22477	−	6.22477i	−0.231182	−	0.231182i
$726$	−0.440628	+	0.440628i	−0.0163532	+	0.0163532i
$727$	−42.4141			−1.57305			−0.786525	−	0.617558i	$-0.788122\pi$
$727$	−42.4141			−1.57305			−0.786525	+	0.617558i	$0.788122\pi$
$728$	42.1451	−	42.1451i	1.56200	−	1.56200i
$729$			24.7365i			0.916167i
$730$	−3.04305			−0.112628
$731$	−11.1319	−	2.11126i	−0.411728	−	0.0780879i
$732$	2.51062			0.0927951
$733$		−	43.4227i		−	1.60386i	−0.597421	−	0.801928i	$-0.703808\pi$
$733$		−	43.4227i		−	1.60386i	0.597421	−	0.801928i	$-0.296192\pi$
$734$	34.2062	−	34.2062i	1.26258	−	1.26258i
$735$	5.51088			0.203272
$736$	−0.341793	+	0.341793i	−0.0125987	+	0.0125987i
$737$	−4.22245	−	4.22245i	−0.155536	−	0.155536i
$738$	16.1150	+	16.1150i	0.593202	+	0.593202i
$739$			28.0864i			1.03318i	0.856234	+	0.516588i	$0.172798\pi$
$739$			28.0864i			1.03318i	−0.856234	+	0.516588i	$0.827202\pi$
$740$		−	2.67804i		−	0.0984468i
$741$	4.21277	+	4.21277i	0.154760	+	0.154760i
$742$	−7.78583	−	7.78583i	−0.285827	−	0.285827i
$743$	−31.9613	+	31.9613i	−1.17254	+	1.17254i	−0.190944	+	0.981601i	$0.561155\pi$
$743$	−31.9613	+	31.9613i	−1.17254	+	1.17254i	−0.981601	+	0.190944i	$0.938845\pi$
$744$	52.5818			1.92774
$745$	−0.893798	+	0.893798i	−0.0327462	+	0.0327462i
$746$		−	51.0340i		−	1.86849i
$747$	5.11134			0.187014
$748$	−48.2905	+	32.8933i	−1.76568	+	1.20270i
$749$	29.0110			1.06004
$750$			3.15213i			0.115100i
$751$	17.0168	−	17.0168i	0.620952	−	0.620952i	−0.324823	−	0.945775i	$-0.605305\pi$
$751$	17.0168	−	17.0168i	0.620952	−	0.620952i	0.945775	+	0.324823i	$0.105305\pi$
$752$	−71.1931			−2.59614
$753$	−19.9879	+	19.9879i	−0.728399	+	0.728399i
$754$	99.3866	+	99.3866i	3.61945	+	3.61945i
$755$	−11.4697	−	11.4697i	−0.417426	−	0.417426i
$756$			38.6634i			1.40617i
$757$			18.0018i			0.654285i	0.944975	+	0.327143i	$0.106086\pi$
$757$			18.0018i			0.654285i	−0.944975	+	0.327143i	$0.893914\pi$
$758$	60.9335	+	60.9335i	2.21320	+	2.21320i
$759$	0.417488	+	0.417488i	0.0151539	+	0.0151539i
$760$	−3.06832	+	3.06832i	−0.111300	+	0.111300i
$761$	23.4172			0.848874			0.424437	−	0.905458i	$-0.360472\pi$
$761$	23.4172			0.848874			0.424437	+	0.905458i	$0.360472\pi$
$762$	33.8338	−	33.8338i	1.22567	−	1.22567i
$763$			9.38575i			0.339787i
$764$	−48.6145			−1.75881
$765$	−4.85860	+	3.30946i	−0.175663	+	0.119654i
$766$	−53.5685			−1.93551
$767$			80.5938i			2.91007i
$768$	28.2569	−	28.2569i	1.01963	−	1.01963i
$769$	9.52627			0.343526			0.171763	−	0.985138i	$-0.445054\pi$
$769$	9.52627			0.343526			0.171763	+	0.985138i	$0.445054\pi$
$770$	9.42860	−	9.42860i	0.339783	−	0.339783i
$771$	1.68989	+	1.68989i	0.0608598	+	0.0608598i
$772$	−13.9688	−	13.9688i	−0.502746	−	0.502746i
$773$		−	20.0047i		−	0.719519i	−0.933045	−	0.359759i	$-0.882859\pi$
$773$		−	20.0047i		−	0.719519i	0.933045	−	0.359759i	$-0.117141\pi$
$774$		−	9.84337i		−	0.353813i
$775$	−5.10259	−	5.10259i	−0.183290	−	0.183290i
$776$	28.6177	+	28.6177i	1.02732	+	1.02732i
$777$	0.889860	−	0.889860i	0.0319235	−	0.0319235i
$778$	29.5653			1.05997
$779$	−3.36142	+	3.36142i	−0.120435	+	0.120435i
$780$		−	34.3803i		−	1.23101i
$781$	13.9927			0.500698
$782$	−0.834919	−	1.22574i	−0.0298566	−	0.0438324i
$783$	−48.8833			−1.74695
$784$		−	26.2093i		−	0.936046i
$785$	−6.02893	+	6.02893i	−0.215182	+	0.215182i
$786$	−6.24912			−0.222899
$787$	−12.8060	+	12.8060i	−0.456484	+	0.456484i	−0.897500	−	0.441015i	$-0.854618\pi$
$787$	−12.8060	+	12.8060i	−0.456484	+	0.456484i	0.441015	+	0.897500i	$0.354618\pi$
$788$	40.3909	+	40.3909i	1.43887	+	1.43887i
$789$	6.92179	+	6.92179i	0.246422	+	0.246422i
$790$		−	12.6840i		−	0.451275i
$791$		−	15.0135i		−	0.533819i
$792$	−19.2439	−	19.2439i	−0.683804	−	0.683804i
$793$	2.08555	+	2.08555i	0.0740600	+	0.0740600i
$794$	−5.96708	+	5.96708i	−0.211764	+	0.211764i
$795$	−3.40525			−0.120772
$796$	8.04395	−	8.04395i	0.285110	−	0.285110i
$797$			44.1981i			1.56558i	0.622289	+	0.782788i	$0.286203\pi$
$797$			44.1981i			1.56558i	−0.622289	+	0.782788i	$0.713797\pi$
$798$	−3.80324			−0.134633
$799$	9.16631	−	48.3306i	0.324281	−	1.70981i
$800$	3.37606			0.119362
$801$		−	15.0999i		−	0.533527i
$802$	4.60882	−	4.60882i	0.162743	−	0.162743i
$803$	3.98102			0.140487
$804$	6.94999	−	6.94999i	0.245107	−	0.245107i
$805$	0.163488	+	0.163488i	0.00576219	+	0.00576219i
$806$	81.4695	+	81.4695i	2.86964	+	2.86964i
$807$			17.2443i			0.607029i
$808$			3.94581i			0.138813i
$809$	−14.4229	−	14.4229i	−0.507083	−	0.507083i	0.406547	−	0.913630i	$-0.366733\pi$
$809$	−14.4229	−	14.4229i	−0.507083	−	0.507083i	−0.913630	+	0.406547i	$0.866733\pi$
$810$	4.77834	+	4.77834i	0.167894	+	0.167894i
$811$	−1.48389	+	1.48389i	−0.0521064	+	0.0521064i	−0.732680	−	0.680573i	$-0.761731\pi$
$811$	−1.48389	+	1.48389i	−0.0521064	+	0.0521064i	0.680573	+	0.732680i	$0.261731\pi$
$812$	−61.2937			−2.15099
$813$	11.0770	−	11.0770i	0.388488	−	0.388488i
$814$			5.12865i			0.179759i
$815$	−15.4603			−0.541551
$816$	−17.3781	−	25.5128i	−0.608356	−	0.893125i
$817$	2.05322			0.0718332
$818$		−	77.4704i		−	2.70869i
$819$	−10.3467	+	10.3467i	−0.361543	+	0.361543i
$820$	27.4325			0.957985
$821$	−3.49477	+	3.49477i	−0.121968	+	0.121968i	−0.765456	−	0.643488i	$-0.777487\pi$
$821$	−3.49477	+	3.49477i	−0.121968	+	0.121968i	0.643488	+	0.765456i	$0.277487\pi$
$822$	−43.7060	−	43.7060i	−1.52442	−	1.52442i
$823$	8.09920	+	8.09920i	0.282320	+	0.282320i	0.834034	−	0.551713i	$-0.186026\pi$
$823$	8.09920	+	8.09920i	0.282320	+	0.282320i	−0.551713	+	0.834034i	$0.686026\pi$
$824$			0.908630i			0.0316536i
$825$		−	4.12374i		−	0.143570i
$826$	−36.3796	−	36.3796i	−1.26581	−	1.26581i
$827$	−13.6785	−	13.6785i	−0.475647	−	0.475647i	0.428090	−	0.903736i	$-0.359187\pi$
$827$	−13.6785	−	13.6785i	−0.475647	−	0.475647i	−0.903736	+	0.428090i	$0.859187\pi$
$828$	0.622374	−	0.622374i	0.0216290	−	0.0216290i
$829$	26.7634			0.929530			0.464765	−	0.885434i	$-0.346139\pi$
$829$	26.7634			0.929530			0.464765	+	0.885434i	$0.346139\pi$
$830$	6.36853	−	6.36853i	0.221055	−	0.221055i
$831$		−	33.7009i		−	1.16907i
$832$	21.9422			0.760708
$833$	17.7926	+	3.37452i	0.616477	+	0.116920i
$834$	11.3836			0.394182
$835$			3.67070i			0.127030i
$836$	7.48697	−	7.48697i	0.258942	−	0.258942i
$837$	−40.0708			−1.38505
$838$	−33.1617	+	33.1617i	−1.14555	+	1.14555i
$839$	37.0327	+	37.0327i	1.27851	+	1.27851i	0.941502	+	0.337008i	$0.109415\pi$
$839$	37.0327	+	37.0327i	1.27851	+	1.27851i	0.337008	+	0.941502i	$0.390585\pi$
$840$	8.32045	+	8.32045i	0.287083	+	0.287083i
$841$		−	48.4956i		−	1.67226i
$842$		−	74.2876i		−	2.56012i
$843$	13.7772	+	13.7772i	0.474513	+	0.474513i
$844$	−21.7529	−	21.7529i	−0.748766	−	0.748766i
$845$	19.3670	−	19.3670i	0.666247	−	0.666247i
$846$	42.7362			1.46930
$847$	0.225735	−	0.225735i	0.00775635	−	0.00775635i
$848$			16.1951i			0.556141i
$849$	13.0982			0.449531
$850$	−1.93017	+	10.1771i	−0.0662043	+	0.349071i
$851$	−0.0889284			−0.00304843
$852$			23.0314i			0.789043i
$853$	0.0880569	−	0.0880569i	0.00301501	−	0.00301501i	−0.705598	−	0.708613i	$-0.749321\pi$
$853$	0.0880569	−	0.0880569i	0.00301501	−	0.00301501i	0.708613	+	0.705598i	$0.249321\pi$
$854$	−1.88281			−0.0644285
$855$	0.753279	−	0.753279i	0.0257616	−	0.0257616i
$856$	−73.7758	−	73.7758i	−2.52160	−	2.52160i
$857$	−15.9912	−	15.9912i	−0.546249	−	0.546249i	0.379104	−	0.925354i	$-0.376232\pi$
$857$	−15.9912	−	15.9912i	−0.546249	−	0.546249i	−0.925354	+	0.379104i	$0.876232\pi$
$858$			65.8408i			2.24777i
$859$			38.2254i			1.30423i	0.758118	+	0.652117i	$0.226119\pi$
$859$			38.2254i			1.30423i	−0.758118	+	0.652117i	$0.773881\pi$
$860$	−8.37817	−	8.37817i	−0.285693	−	0.285693i
$861$	9.11527	+	9.11527i	0.310648	+	0.310648i
$862$	−29.0380	+	29.0380i	−0.989037	+	0.989037i
$863$	−22.1777			−0.754939			−0.377469	−	0.926022i	$-0.623206\pi$
$863$	−22.1777			−0.754939			−0.377469	+	0.926022i	$0.623206\pi$
$864$	13.2562	−	13.2562i	0.450984	−	0.450984i
$865$			9.14139i			0.310816i
$866$	−35.9904			−1.22300
$867$	19.5572	−	8.51258i	0.664198	−	0.289102i
$868$	−50.2438			−1.70539
$869$			16.5936i			0.562901i
$870$	−19.6213	+	19.6213i	−0.665225	+	0.665225i
$871$	11.5466			0.391241
$872$	23.8682	−	23.8682i	0.808279	−	0.808279i
$873$	−7.02571	−	7.02571i	−0.237784	−	0.237784i
$874$	0.190039	+	0.190039i	0.00642817	+	0.00642817i
$875$		−	1.61485i		−	0.0545918i
$876$			6.55261i			0.221392i
$877$	19.1327	+	19.1327i	0.646067	+	0.646067i	0.952040	−	0.305973i	$-0.0989819\pi$
$877$	19.1327	+	19.1327i	0.646067	+	0.646067i	−0.305973	+	0.952040i	$0.598982\pi$
$878$	−54.0565	−	54.0565i	−1.82432	−	1.82432i
$879$	−6.30478	+	6.30478i	−0.212655	+	0.212655i
$880$	−19.6121			−0.661125
$881$	−26.0576	+	26.0576i	−0.877903	+	0.877903i	−0.993317	−	0.115414i	$-0.963180\pi$
$881$	−26.0576	+	26.0576i	−0.877903	+	0.877903i	0.115414	+	0.993317i	$0.463180\pi$
$882$			15.7331i			0.529760i
$883$	20.6901			0.696277			0.348138	−	0.937443i	$-0.386814\pi$
$883$	20.6901			0.696277			0.348138	+	0.937443i	$0.386814\pi$
$884$	21.0524	−	111.001i	0.708068	−	3.73338i
$885$	−15.9112			−0.534848
$886$			66.5851i			2.23697i
$887$	−10.5540	+	10.5540i	−0.354368	+	0.354368i	−0.861732	−	0.507364i	$-0.830620\pi$
$887$	−10.5540	+	10.5540i	−0.354368	+	0.354368i	0.507364	+	0.861732i	$0.330620\pi$
$888$	−4.52587			−0.151878
$889$	−17.3332	+	17.3332i	−0.581336	+	0.581336i
$890$	−18.8138	−	18.8138i	−0.630640	−	0.630640i
$891$	−6.25121	−	6.25121i	−0.209423	−	0.209423i
$892$		−	52.4770i		−	1.75706i
$893$			8.91433i			0.298307i
$894$	2.81737	+	2.81737i	0.0942270	+	0.0942270i
$895$	6.19523	+	6.19523i	0.207084	+	0.207084i
$896$	−17.6146	+	17.6146i	−0.588463	+	0.588463i
$897$	−1.14165			−0.0381186
$898$	−28.1376	+	28.1376i	−0.938963	+	0.938963i
$899$		−	63.5249i		−	2.11867i
$900$	−6.14750			−0.204917
$901$	−10.9943	−	2.08516i	−0.366273	−	0.0694668i
$902$	−52.5352			−1.74923
$903$		−	5.56779i		−	0.185285i
$904$	−38.1797	+	38.1797i	−1.26984	+	1.26984i
$905$	4.86717			0.161790
$906$	−36.1541	+	36.1541i	−1.20114	+	1.20114i
$907$	−19.3243	−	19.3243i	−0.641653	−	0.641653i	0.309309	−	0.950962i	$-0.399902\pi$
$907$	−19.3243	−	19.3243i	−0.641653	−	0.641653i	−0.950962	+	0.309309i	$0.899902\pi$
$908$	2.54769	+	2.54769i	0.0845481	+	0.0845481i
$909$		−	0.968706i		−	0.0321299i
$910$			25.7832i			0.854703i
$911$	33.4927	+	33.4927i	1.10966	+	1.10966i	0.993194	+	0.116469i	$0.0371575\pi$
$911$	33.4927	+	33.4927i	1.10966	+	1.10966i	0.116469	+	0.993194i	$0.462843\pi$
$912$	3.95550	+	3.95550i	0.130980	+	0.130980i
$913$	−8.33154	+	8.33154i	−0.275734	+	0.275734i
$914$	10.6860			0.353463
$915$	−0.411737	+	0.411737i	−0.0136116	+	0.0136116i
$916$			26.4486i			0.873888i
$917$	3.20145			0.105721
$918$	32.3816	+	47.5393i	1.06875	+	1.56903i
$919$	25.7946			0.850884			0.425442	−	0.904986i	$-0.360119\pi$
$919$	25.7946			0.850884			0.425442	+	0.904986i	$0.360119\pi$
$920$		−	0.831507i		−	0.0274140i
$921$	−4.26306	+	4.26306i	−0.140473	+	0.140473i
$922$	60.2300			1.98357
$923$	−19.1320	+	19.1320i	−0.629737	+	0.629737i
$924$	−20.3027	−	20.3027i	−0.667909	−	0.667909i
$925$	0.439195	+	0.439195i	0.0144406	+	0.0144406i
$926$			57.8150i			1.89992i
$927$		−	0.223071i		−	0.00732660i
$928$	21.0152	+	21.0152i	0.689858	+	0.689858i
$929$	−17.4671	−	17.4671i	−0.573076	−	0.573076i	0.359911	−	0.932987i	$-0.382807\pi$
$929$	−17.4671	−	17.4671i	−0.573076	−	0.573076i	−0.932987	+	0.359911i	$0.882807\pi$
$930$	−16.0840	+	16.0840i	−0.527416	+	0.527416i
$931$	−3.28175			−0.107555
$932$	51.3330	−	51.3330i	1.68147	−	1.68147i
$933$		−	10.0742i		−	0.329815i
$934$	54.7292			1.79080
$935$	2.52512	−	13.3140i	0.0825802	−	0.435415i
$936$	52.6239			1.72007
$937$			37.0383i			1.20999i	0.796230	+	0.604994i	$0.206825\pi$
$937$			37.0383i			1.20999i	−0.796230	+	0.604994i	$0.793175\pi$
$938$	−5.21207	+	5.21207i	−0.170180	+	0.170180i
$939$	−27.7309			−0.904964
$940$	36.3749	−	36.3749i	1.18642	−	1.18642i
$941$	24.2477	+	24.2477i	0.790452	+	0.790452i	0.981568	−	0.191115i	$-0.0612104\pi$
$941$	24.2477	+	24.2477i	0.790452	+	0.790452i	−0.191115	+	0.981568i	$0.561210\pi$
$942$	19.0040	+	19.0040i	0.619183	+	0.619183i
$943$		−	0.910938i		−	0.0296642i
$944$			75.6721i			2.46292i
$945$	−6.34073	−	6.34073i	−0.206264	−	0.206264i
$946$	16.0448	+	16.0448i	0.521661	+	0.521661i
$947$	26.2345	−	26.2345i	0.852507	−	0.852507i	−0.137934	−	0.990441i	$-0.544046\pi$
$947$	26.2345	−	26.2345i	0.852507	−	0.852507i	0.990441	+	0.137934i	$0.0440462\pi$
$948$	−27.3125			−0.887068
$949$	−5.44319	+	5.44319i	−0.176694	+	0.176694i
$950$		−	1.87711i		−	0.0609015i
$951$	20.0306			0.649537
$952$	21.7687	+	31.9586i	0.705529	+	1.03578i
$953$	26.9203			0.872033			0.436016	−	0.899939i	$-0.356389\pi$
$953$	26.9203			0.872033			0.436016	+	0.899939i	$0.356389\pi$
$954$		−	9.72168i		−	0.314751i
$955$	7.97270	−	7.97270i	0.257991	−	0.257991i
$956$	−29.9791			−0.969592
$957$	25.6693	−	25.6693i	0.829771	−	0.829771i
$958$	−58.4997	−	58.4997i	−1.89004	−	1.89004i
$959$	22.3907	+	22.3907i	0.723035	+	0.723035i
$960$			4.33191i			0.139812i
$961$		−	21.0728i		−	0.679768i
$962$	−7.01232	−	7.01232i	−0.226086	−	0.226086i
$963$	18.1121	+	18.1121i	0.583655	+	0.583655i
$964$	93.6641	−	93.6641i	3.01672	−	3.01672i
$965$	4.58171			0.147490
$966$	0.515335	−	0.515335i	0.0165806	−	0.0165806i
$967$			26.4462i			0.850452i	0.905087	+	0.425226i	$0.139805\pi$
$967$			26.4462i			0.850452i	−0.905087	+	0.425226i	$0.860195\pi$
$968$	−1.14810			−0.0369014
$969$	−3.19454	+	2.17597i	−0.102623	+	0.0699024i
$970$	−17.5075			−0.562132
$971$			9.69327i			0.311072i	0.987830	+	0.155536i	$0.0497104\pi$
$971$			9.69327i			0.311072i	−0.987830	+	0.155536i	$0.950290\pi$
$972$	−40.5003	+	40.5003i	−1.29905	+	1.29905i
$973$	−5.83185			−0.186961
$974$	33.1283	−	33.1283i	1.06150	−	1.06150i
$975$	5.63832	+	5.63832i	0.180571	+	0.180571i
$976$	1.95819	+	1.95819i	0.0626801	+	0.0626801i
$977$		−	5.81399i		−	0.186006i	−0.995666	−	0.0930029i	$-0.970353\pi$
$977$		−	5.81399i		−	0.186006i	0.995666	−	0.0930029i	$-0.0296466\pi$
$978$			48.7329i			1.55831i
$979$	24.6129	+	24.6129i	0.786632	+	0.786632i
$980$	13.3912	+	13.3912i	0.427765	+	0.427765i
$981$	−5.85970	+	5.85970i	−0.187086	+	0.187086i
$982$	9.98153			0.318523
$983$	22.4102	−	22.4102i	0.714776	−	0.714776i	−0.252755	−	0.967530i	$-0.581337\pi$
$983$	22.4102	−	22.4102i	0.714776	−	0.714776i	0.967530	+	0.252755i	$0.0813366\pi$
$984$		−	46.3608i		−	1.47793i
$985$	−13.2481			−0.422119
$986$	−75.3648	+	51.3351i	−2.40010	+	1.63484i
$987$	24.1733			0.769443
$988$			20.4736i			0.651353i
$989$	−0.278210	+	0.278210i	−0.00884655	+	0.00884655i
$990$	11.7729			0.374167
$991$	34.2715	−	34.2715i	1.08867	−	1.08867i	0.0930058	−	0.995666i	$-0.470352\pi$
$991$	34.2715	−	34.2715i	1.08867	−	1.08867i	0.995666	−	0.0930058i	$-0.0296475\pi$
$992$	17.2266	+	17.2266i	0.546946	+	0.546946i
$993$	3.44152	+	3.44152i	0.109213	+	0.109213i
$994$		−	17.2722i		−	0.547840i
$995$			2.63839i			0.0836426i
$996$	−13.7134	−	13.7134i	−0.434526	−	0.434526i
$997$	4.30543	+	4.30543i	0.136354	+	0.136354i	0.771990	−	0.635635i	$-0.219262\pi$
$997$	4.30543	+	4.30543i	0.136354	+	0.136354i	−0.635635	+	0.771990i	$0.719262\pi$
$998$	60.6283	−	60.6283i	1.91916	−	1.91916i
$999$	3.44901			0.109122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.e.a.21.6	✓	12
3.2	odd	2		765.2.k.b.361.1		12
4.3	odd	2		1360.2.bt.d.1041.4		12
5.2	odd	4		425.2.j.b.174.1		12
5.3	odd	4		425.2.j.c.174.6		12
5.4	even	2		425.2.e.f.276.1		12
17.2	even	8		1445.2.d.g.866.2		12
17.8	even	8		1445.2.a.o.1.6		6
17.9	even	8		1445.2.a.n.1.6		6
17.13	even	4	inner	85.2.e.a.81.1	yes	12
17.15	even	8		1445.2.d.g.866.1		12
51.47	odd	4		765.2.k.b.676.6		12
68.47	odd	4		1360.2.bt.d.81.4		12
85.9	even	8		7225.2.a.bb.1.1		6
85.13	odd	4		425.2.j.b.149.1		12
85.47	odd	4		425.2.j.c.149.6		12
85.59	even	8		7225.2.a.z.1.1		6
85.64	even	4		425.2.e.f.251.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.6	✓	12	1.1	even	1	trivial
85.2.e.a.81.1	yes	12	17.13	even	4	inner
425.2.e.f.251.6		12	85.64	even	4
425.2.e.f.276.1		12	5.4	even	2
425.2.j.b.149.1		12	85.13	odd	4
425.2.j.b.174.1		12	5.2	odd	4
425.2.j.c.149.6		12	85.47	odd	4
425.2.j.c.174.6		12	5.3	odd	4
765.2.k.b.361.1		12	3.2	odd	2
765.2.k.b.676.6		12	51.47	odd	4
1360.2.bt.d.81.4		12	68.47	odd	4
1360.2.bt.d.1041.4		12	4.3	odd	2
1445.2.a.n.1.6		6	17.9	even	8
1445.2.a.o.1.6		6	17.8	even	8
1445.2.d.g.866.1		12	17.15	even	8
1445.2.d.g.866.2		12	17.2	even	8
7225.2.a.z.1.1		6	85.59	even	8
7225.2.a.bb.1.1		6	85.9	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.51230i q^{2} +(-0.887192 + 0.887192i) q^{3} -4.31167 q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.22889 - 2.22889i) q^{6} +(1.14187 + 1.14187i) q^{7} -5.80761i q^{8} +1.42578i q^{9} +(1.77647 + 1.77647i) q^{10} +(-2.32404 - 2.32404i) q^{11} +(3.82528 - 3.82528i) q^{12} +6.35524 q^{13} +(-2.86872 + 2.86872i) q^{14} +1.25468i q^{15} +5.96715 q^{16} +(-0.768287 + 4.05089i) q^{17} -3.58200 q^{18} -0.747167i q^{19} +(-3.04881 + 3.04881i) q^{20} -2.02612 q^{21} +(5.83869 - 5.83869i) q^{22} +(0.101240 + 0.101240i) q^{23} +(5.15247 + 5.15247i) q^{24} -1.00000i q^{25} +15.9663i q^{26} +(-3.92652 - 3.92652i) q^{27} +(-4.92337 - 4.92337i) q^{28} +(6.22477 - 6.22477i) q^{29} -3.15213 q^{30} +(5.10259 - 5.10259i) q^{31} +3.37606i q^{32} +4.12374 q^{33} +(-10.1771 - 1.93017i) q^{34} +1.61485 q^{35} -6.14750i q^{36} +(-0.439195 + 0.439195i) q^{37} +1.87711 q^{38} +(-5.63832 + 5.63832i) q^{39} +(-4.10660 - 4.10660i) q^{40} +(-4.49889 - 4.49889i) q^{41} -5.09022i q^{42} +2.74801i q^{43} +(10.0205 + 10.0205i) q^{44} +(1.00818 + 1.00818i) q^{45} +(-0.254346 + 0.254346i) q^{46} -11.9308 q^{47} +(-5.29400 + 5.29400i) q^{48} -4.39226i q^{49} +2.51230 q^{50} +(-2.91230 - 4.27554i) q^{51} -27.4017 q^{52} +2.71404i q^{53} +(9.86460 - 9.86460i) q^{54} -3.28669 q^{55} +(6.63154 - 6.63154i) q^{56} +(0.662880 + 0.662880i) q^{57} +(15.6385 + 15.6385i) q^{58} +12.6815i q^{59} -5.40976i q^{60} +(0.328162 + 0.328162i) q^{61} +(12.8193 + 12.8193i) q^{62} +(-1.62806 + 1.62806i) q^{63} +3.45261 q^{64} +(4.49384 - 4.49384i) q^{65} +10.3601i q^{66} +1.81686 q^{67} +(3.31260 - 17.4661i) q^{68} -0.179639 q^{69} +4.05699i q^{70} +(-3.01043 + 3.01043i) q^{71} +8.28039 q^{72} +(-0.856488 + 0.856488i) q^{73} +(-1.10339 - 1.10339i) q^{74} +(0.887192 + 0.887192i) q^{75} +3.22154i q^{76} -5.30750i q^{77} +(-14.1652 - 14.1652i) q^{78} +(-3.57000 - 3.57000i) q^{79} +(4.21941 - 4.21941i) q^{80} +2.68980 q^{81} +(11.3026 - 11.3026i) q^{82} -3.58494i q^{83} +8.73594 q^{84} +(2.32115 + 3.40767i) q^{85} -6.90384 q^{86} +11.0451i q^{87} +(-13.4971 + 13.4971i) q^{88} -10.5906 q^{89} +(-2.53285 + 2.53285i) q^{90} +(7.25687 + 7.25687i) q^{91} +(-0.436515 - 0.436515i) q^{92} +9.05395i q^{93} -29.9739i q^{94} +(-0.528327 - 0.528327i) q^{95} +(-2.99521 - 2.99521i) q^{96} +(-4.92762 + 4.92762i) q^{97} +11.0347 q^{98} +(3.31357 - 3.31357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - 12 q^{4} - 4 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{14} + 4 q^{16} + 12 q^{17} + 28 q^{18} - 8 q^{20} - 16 q^{21} + 20 q^{22} + 12 q^{23} + 4 q^{24} - 4 q^{27} + 4 q^{28} - 12 q^{29} - 8 q^{30}+ \cdots + 44 q^{98}+O(q^{100}) \) 12 * q - 4 * q^3 - 12 * q^4 - 4 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^14 + 4 * q^16 + 12 * q^17 + 28 * q^18 - 8 * q^20 - 16 * q^21 + 20 * q^22 + 12 * q^23 + 4 * q^24 - 4 * q^27 + 4 * q^28 - 12 * q^29 - 8 * q^30 - 16 * q^33 - 12 * q^34 + 16 * q^35 + 12 * q^37 + 24 * q^38 - 20 * q^39 - 8 * q^40 - 24 * q^41 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 48 * q^47 - 20 * q^48 + 4 * q^50 + 32 * q^51 - 56 * q^52 + 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 + 40 * q^62 + 12 * q^63 + 28 * q^64 + 4 * q^65 - 8 * q^67 - 40 * q^68 + 28 * q^71 + 20 * q^72 - 48 * q^73 + 28 * q^74 + 4 * q^75 - 92 * q^78 - 8 * q^79 + 16 * q^80 + 28 * q^81 + 40 * q^82 - 4 * q^85 - 96 * q^86 - 72 * q^88 + 24 * q^89 - 16 * q^90 - 36 * q^91 - 16 * q^92 - 8 * q^95 - 32 * q^96 + 4 * q^97 + 44 * q^98

Introduction

L-functions

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